The study found disturbing evidence of young Muslims adopting more fundamentalist beliefs on key social and political issues than their parents or grandparents.

Forty per cent of Muslims between the ages of 16 and 24 said they would prefer to live under sharia law in Britain, a legal system based on the teachings of the Koran. The figure among over-55s, in contrast, was only 17 per cent.

In some countries, people found guilty under sharia law face penalties such as beheading, stoning, the severing of a hand or being lashed.

The study, by the Right-wing think-tank Policy Exchange, also found a significant minority who expressed backing for Islamic terrorism.

One in eight young Muslims said they admired groups such as al-Qa'eda that "are prepared to fight the West".

Turning to issues of faith, 36 per cent of the young people questioned said they believed that a Muslim who converts to another religion should be "punished by death." Among the over 55s, the figure is only 19 per cent.

Three out of four young Muslims would prefer Muslim women to "choose to wear the veil or hijab," compared to only a quarter of over-55s.

Support was also strong for Islamic schools, according to the Populus survey of 1,000 people commissioned by Policy Exchange.

Forty per cent of younger Muslims said they would want their children to attend an Islamic school, compared to only 20 per cent of over-55s.

Britain's foreign policies were a key issue among the Muslim population as a whole, with 58 per cent arguing that many of the world's problems are "a result of arrogant Western attitudes". However, knowledge of foreign affairs was sketchy, with only one in five knowing that Mahmoud Abbas was the Palestinian president.

The findings emerged as David Cameron, the Conservative leader, criticised the Government for trying to "bully" immigrant communities into feeling British by telling them to run up the Union flag in their gardens or spy on their children.

But in a speech today, Mr Cameron will warn the Muslim community that it cannot use the "screen of cultural sensitivity" to deny women their rights.

The Policy Exchange report, Living Together Apart: British Muslims and the Paradox of Multiculturalism — says there is strong evidence of a "growing religiosity" among young Muslims, with an increasing minority firmly rejecting Western life.

Munira Mirza, the broadcaster and one of the authors of the report, argued that multicultural policies pursued by the Government had succeeded in making things worse, rather than better.

She said: "The emergence of a strong Muslim identity in Britain is, in part, a result of multi-cultural policies implemented since the 1980s which have emphasised difference at the expense of shared national identity and divided people along ethnic, religious and cultural lines.

"There is clearly a conflict within British Islam between a moderate majority that accepts the norms of British democracy and a growing minority that does not."

The report also raises questions about the scale of the problems created by Islamophobia, with 84 per cent of those questioned saying they believed they had been "treated fairly" in Britain.

There was also criticism of the decision by some councils to ban Christian symbols in case they offended Muslims or other communities.

Three quarters said it was wrong for a council to have banned an advert for a Christmas carol service.

Shahid Malik, the Muslim Labour MP for Dewsbury, said: "This report makes very disturbing reading and it vindicates the concern many of us have that we're not doing enough to confront this issue."

Baroness Uddin, the Muslim peer, said: "Unlike their parents, our young people feel that this is their country and are saying why are we being told we do not belong here.

"There is also a problem of a lack of opportunities. Some people have been brutalised by their experiences with the police and this war on terror."

In his speech in Birmingham today, Mr Cameron will criticise "simplistic" attempts at community cohesion, such as Gordon Brown's call for people to put up the Union flag.

But he will also challenge elements of the Muslim community for denying women access to work, education, politics and even to mosques.

In a move that will please the Tory Right, Mr Cameron will warn that urgent action must be taken to get a grip of an immigration system that is out of control.

"It's the same whether it's the white grandmother worried about groups of asylum seekers or an unemployed Sikh youngster who sees eastern Europeans filling all the jobs.

"The Government needs to be in control of the situation. We can only live together if there is proper integration.

"And you can't have proper integration if people are coming into Britain at a faster rate than we can cope with."